NO-ABEL 2003 Problem 3

Let $ABC$ be a triangle with $AC> BC$ , and let $S$ be the circumscribed circle of the triangle. $AB$ divides $S$ into two arcs. Let $D$ be the midpoint of the arc containing $C$ . (a) Show that $\angle ACB +2 \cdot \angle ACD = 180^o$ . (b) Let $E$ be the foot of the altitude from $D$ on $AC$ . Show that $BC +CE = AE$ .